Numerical calculating device



G. G. DOBSON.

NUMEBICAL CALCULATING DEVICE. APPLICATION FILED IAN. 2, IsIs.

Patented Aug. 22, 1922..

like.

UNITED s'rA'rEs GEORGE G. DOBSON, 0F PASSAIC, NEW JERSEY, ASSIGNO-R T0 PATENT OFFICE.

WESTERN ELECTRIC COMPANY, INCORPORATED, or NEW YORK, N. Y., A cORrOnATION OF NEW YORK.

NUMERIGAL CALCULATING DEVICE.

Specification of Letters Patent.

Patented Aug. 22, 1922.

Appucatmn'mea January 2, 191s. serial No. 209,965.

To allfwhom it may concern:

Be it known that I, GEORGE GORDON DOB- SON a citizen of the United States, residing at Rassaic, in the county of Passaic, State of New Jersey, have invented certain new and useful Improvements in Numerical Calculating Devices, of which the followin is a full, clear, concise, and exact description.

This invention relates to a numerical calculating device and is more. particularly described as a slide rule.

An Object of this invention "is to provide a device of this class for the direct solution of .problems involving second degree equations. y

A further Object is to provide a device for obtaining winding calculations directly, such as computations relating to the winding of lamentary material on spools, or the Although this inventionwill be hereinafter described as especially adapted to the computations relating to the 'winding of conductors on spools to form relay coils, for

example, it is to be understood that it is not so limited, since it has wide application, as will be apparent from the detailed description and drawings. For the purpose of this specification, the. phrase, filamem tary material, will be em loyed to be broadly descriptive of materia made in any such form as that of a cord, thread, wire, strand, ribbon, rope, strin and the like.

In manufacturing spoo s having a conductor wound thereon, it is desirable to previously determine various data before actually performing the winding of the conductor, such as, for example, determining how many layers of wire of a given -size may be wound on a certain size spool, or whvat size of wire should be employed to give a specified resistance when the spool is wound full, and other such calculations.

Assume that it is desired to wind a wire ofa given size u on a spool having a length L and a, depth available forl winding on acore of diameter d.

.If N be the total number of turns of wire having a. resistance 1' per unit length that may be Woundl on this spool, then the total resistance R of N number of turns would be l actually required for one turn, then may wrlte the above'expreion as L-Dvrr n K (Dld smce 142 N If we call vrr S then R=LDS(D+Z) which may be written LS 2 Dd and since NK D= R NZK2 NKd LsT2 *"T dividing this' by d2 we Obtain R NZK2 NK Lksdfw "L L If we call n Q vthen and then if we call If it be desired, for example, to determine `the value of N ,-the method to be followed would be to find first the Value of Q', as-

suming the values of R, L, S and d to be is then necessary to i'ind Q by solving the quadratic equation QzQQd-ll Knowing Q, N may then be obtained trom the expression Qdf TT la For some of the calculations in regard to winding coils, 1t has been found convenient to employ a single expression c for' the ratio E where D is the depth ci the winding of the spool and n the number of layers of a given size of material that may be wound thereon. For example, ii we have given the number of layers desired and know the dimensions of the spool and the size of wire desired, we may obtain the total resistance the wire would have by first tinding the value of Q from the .expression That this expression: is true may be seen from the fact that NK D 0n Q=- one face of the rule; Fig. 2 illustrates the reverse side; Fig. 3 illustrates how the rule may be set for the solution of quadratic equations; and Fig. 4 is a cross-sectional view of the rule).

Referring to Figs. 1 and 2, it will be seen that the slide rule illustrated therein has three slides 5, 6 and 7, which work in suitable grooves in the framework of the rule comprising the bars 8, 9 and 10 which are held together by cross pieces 11, 12, 13 and 14. 15 is the runner for theslide rule.

Referring particularl to Fig. 1, which shows one Jface A of t e rule, on the bar 8 are two ordinary inverted logarithmic scales set end to end and marked L on the cross piece 11. On the slide 5, and marked R, are shown three logarithmic scales set end to end and each of the same length i ,ceases as the scales marked L. @n the bar 9 are two logarithmic scales similar to each other set end to end. @n vthe upper bar oi slide 6 are values of S plotted according to their logarithmic values which may be markedv as shown in terms of the size oi wire *for the various values. @n the lower part oi' the slide d is an inverted logarithmic scale and of a length double that of the logarithmic scales shown on either scale R or li and marked 3% on the cross piece 11 @n the bar 10 is a scale showing values ci Q which correspond toI values ofQ(Q-l1) on Y rithmic values and marked as shown in terms of the vsize oi' wire for the various values on a logarithmic scale oi length equivalent to the scale length oit' Q. 0n the lower sideof the slide Z are two ordinary logarithmic scales set end to end and marked d, n, D. The bar 9 has on it a scale of values of c expressed in terms of size of wire and plotted according to their logarithmic values on this scale so that for any size of wire the value of c for it will appear on scalel Q opposite its number on scale c. Slide 5 has'on it three logarithmic scales setend to end and marked N. It is to be. noted that the slide 5 is a so-called duplex slideand has a scale on both faces of the rule so that setting the slide on one side automatically sets it on the other.

As an example of the method to be followed in employing this slide rule for calculations, the slides in the Figs. 1 and 2 are shown to be set for a calculation for the number of turns N of No. 30 wire having a total resistance R of 1100 ohms that may be wound on a spool having a cylindrical core of diameter d 0.395 inches, and windin length L of 3.1 inches.

e have given /y R s vQ (Q+1)=Q :m and we are to find the value of Q from such e uation, and then knowing Q to solve for given that To divide R, which has the value of 1100,

by L, which is equal to 3.1, remembering thatscale L is an inverted scale, unity on scale R (preferably the third unity from the left) is set opposite the value of L on scale L as is shown at arrow mark 20 (Fig. 1). bar 94 opposite 1100 von R, is approximately 355 (under arrow mark 21) which is the result of the division of 1100 by 3.1.

The .next step is then to divide 355 by i the valueof S. The logarithm of the value of S for No. 30 wire should then be subtracted from the logarithm of 355. This may be accomplished as shown at arrowpoint marked 21, by setting the No. 30 on slide 6 ofA scale S under 355 on scale 9, and reading oil' at arrow mark 27 the result, namely, 1.52, which is opposite to unity on scale f We now have to Vdivide 1.52 by the value of d2 which is the square of .395. Since the l scale marked a; 1s an lnverse scale and is of double the length of the scales on bar 9, the division may be accomplished on scale were multiplying 1.52 by (395)?. We then set unity on scale4 (which setting in this case has been previously made) under` 1.52 on scale 9 and read off the value 9.75

value of Q, vunder-the value of i on scale '9 which is opposite .395 on scale which-setting'is shown at position 23 of the runner. We have, therefore, divided R by L, .S and d2, and have obtalned the value '9.75 which'then is the, value of Q.

.And since each value m on scale Q corresponds to a (-l-l) on an ordinary scale as 2.66 on the lower part of scale Q which corresponds' to 9.7 5 on scale 9 is the value of Q which is desired. It" is to be noted that scale Q is a'double scale and whether the result is to be read/0n the upper or lower portion depends upon the position of the decimal point inthe value of Q.

l The above method of finding the Value of. A Q is longer than`ne'ed be in actual practice. For example, thescale' on bar 9, face A, `may be omitted if desired, and the following operations are all that are necessary to obtain the value of Q:` 1)v set the thirdv l `on'scale p, thereby arriving at the same result given above.

The value,ftherefore, on the scale on' Now referring to vface B, Fig. 2, We proceed to solve for N, knowing that and knowing that the setting of duplex slide 5 previously performed has already introduced the multiplier L. We then must multiply Q by 0l and divide the result by K in order to obtain the value of N. We therefore must Set No. 30 on scale K (full line) under 2.66 on scale Q, face B, shown at arrow mark 24and readoff the value of N under 0.395 on scale d,.whicl`1 gives us for N -a value of approximately 26,400 turns.

It is'to be noted that keach slide is set only once in the operation of finding the value of N so that the result may be quickly checked by retracing with the runner the various steps performed'without a single. resetting of any portion of the rule,a very important advantage in above also may be employed to find the value of R, yfor example, knowing that N equals 26,400. The steps outlined above would be retraced backwards until the value of Q on face B was found to be 2.66. Then settin the'hair onthe runner on 2.66 on bar face A, and multiplying by S, d2, and L, the value of R, namely 1100, would be obtained. Other values that were unknown could be calculatedy similarly, such as to 4find the size of wire to be employed or the value of various other data.

In the actual vemployment of this slide rule in the designingof relay coils towhich it is particularly adapted, a Somewhat more `complicated process should preferably be followed in order to insure thebest checking of the results. As the wire employedl may vary somewhat in Iits su posed diameter, it has been found preferab e, to facilitate this checkin to plot the values of the constants K and both for the maximum diameter each given standard gauged wire may have 'and falso for the minimum diameter each may have. In the drawings, the full .line

scale for S and K represents values for the minimum diameter each standard gauged wire may have, while the dotted line scale for -these constants represents values calcu-` lated from the maximum-diameter.

Thus if we lemploy the dotted line values of S and K in suc-h calculations as outlined above we will obtain the minimum values of N and R for a given size of standard gauged wire. On the other hand the use o'f the full lines will give the maximum values for R and N. As an example of the use of the dotted line scales, suppose we havegiven the resistance and the size of wireto be wound on a certain spool Yto test for fullness, that is to test whether such a size of -wire with the required resistance will del mand more than the available winding space on the spool. The value of Q, tace A of the rule, would be found in the way described above under the calculation oi? N, with the exception that the dotted scale ot S would be employed. Setting the value of Q thus obtained on scale Q uface l, we may solve for l), the depthsuch a winding would have, since Qdzl). We may compare the value of D thus obtained with the depth dimension of the spool to vascertain if the spool is over full or not. Since as stated above, the dotted line scale of, S should be employed, the depth of the winding obtained will be the' maximum value for the given size wire or in other Words the value of ll thus obtained is the greatest possible since it is calculated under the most adverse condition of maximum diameter oi the wire.

ln the above examples, it may be noted that all the scales of both sides of the rule were employed in the calculations, exceptslide c may be employed, suppose that the dimensions of the spool and the size of the wire are given to find the values of N and R. ln orderto 'find the number of layers n, that may be wound, We may use the expression Knowing a, e and al, we then may find Q by the expression C e-g the value of which may be read off on scale Q, face B. Setting this value on scale Q,

face A, and multiplying it by Z2 and by S, the value of R may be obtained. Tha value of N may then be obtained as in the first example outlined above.

Fig. 3 illustrates the general use that may be made of scales R and Q, face A, inthe solution of quadratic equations vof the form Z-l-mzb where b is a constant. The scales R and Q provide means whereby such an equation may be solved, since for various values of (w24-) on scale R, the vcorresponding values cfa: have been plotted on scale Q. Therefore, if it is desired to solve a\quadratic equation, say w24-m26, for example, then bypsetting the initial point on the two scales opposite each other, as shown in Fig. 3, the value on scale Q opposite to 6 on R will be tound to be 2. rEhe value of x in the above equation is therefore 2.

An equation of the form w24-wzl), where Landsat a is a constanhniay be also solved since it may be written in the form a2- a a2 Noi/vif We call fz/: and call l= then the above equation becomes y2-l-yzl, which is in the same form as the equation given previously. Setting the value ot K on lt, the corresponding value of y may be found on the scale Q and then knowing the value oi y, the value of a may be determined. r lt is apparent thatl the method applied above may be employed for the solution of still higher degree equations by the suitable plotting ot the scale marked Q. Thus the solution of a cubic equation of the form, say m-f-z-kza, may be solved it the various values of :c on scale Q should be plotted against the corresponding values of rc3-l-2-lon a logarithmic scale, such as scale Similarly equations of the general form a-l-bmg-l-czf may be solved.

lFig. l is a cross sectional view of the rule taken along the plane marked 4, t in Fig. l and illustrates how the slides 5, 6 and 7 may 'be suitably engaged in grooves in the bars 8, 9 and l0 which form the 'framework of the rule. n

lt is to be understood that this invention is not limited to the particular arrangementof scales as shown in the drawing, but that they may be suitably modiied to conform with the particular form of calculation desired without departing in anywise 'from the spirit of this invention as defined in the .appended claims.

lt is to be noted from the above detailed description that face A of the sllde rule is adapted to solve equations ot the general izorm.

farsene with onlyI one resetting; and that ace l3 l is adapted to solve an equation of the form Anc n lio slides representing said variables, whereby r said scales are adapted to cooperate for the determination of an unknown` variable when values of other variables involved in said yproblem are known, one scale on each side of said body being a logarithmic scale,

the scales on both sides of said duplex slide being logarithmic scales.

2. A slide rule for the solution of a problem involving a number of variablesat least one of which is unknown, said rule comprising a body and more than two slides, one of said slides being' a duplex slide, logarithmic scales on said body and each of said slides, each of said scales representing one of said variables whereby said scales are adapted to cooperate for the determination of .an un- Y. known variable when the values of the other variables involved 1n said problem are known. f

3. A slide rule for the solution of a problem relating to the winding of a ilamentary material on a spool involving such duantities as the dimensions of the spool, the size and resistance of the filamentary material,

and the number of turns of said material which may be wound on said spool within the space allowed, said rule comprising a. body and a plurality of slides, one of which is a duplex slide, logarithmic scales on said body and said slides representing said quan'-y tit-ies whereby said scales are adapted to cooperate for the`determination of one of said quantities which is unlmown when the values of other of said quantities involved in the problem are known, said scales being so arranged on said slides and said body that the problem may be solved without the resetting of any one of said slides.

In witness whereof, I hereunto subscribe my name this QSt-hday of December A. D.,

1917. GEORGE G. DOB'SON. 

